A032443 is an analog of the Catalan sequence: Let M denote an infinite Cartan matrix (-1's in the super and sub-diagonals and (2,2,2,...) in the main diagonal which we modify to (1,2,2,2,...). Then A000108 can be generated by accessing the leftmost term in M^n * [1,0,0,0,...]. Change the operation to M^n * [1,2,3,...] to get A032443. Or, take iterates M * [1,2,3,...] -> M * ANS, -> M * ANS,...; accessing the leftmost term. (End)